Problem: The grades on a geometry midterm at Almond are normally distributed with $\mu = 81$ and $\sigma = 4.5$. Luis earned a $94$ on the exam. Find the z-score for Luis's exam grade. Round to two decimal places.
Explanation: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Luis's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{94 - {81}}{{4.5}}} $ ${ z \approx 2.89}$ The z-score is $2.89$. In other words, Luis's score was $2.89$ standard deviations above the mean.